Enlargement of Calderbank Shor Steane quantum codes
Abstract
Description
It is shown that a classical error correcting code C = [n,k,d] which contains its dual, C^{\perp} \subseteq C, and which can be enlarged to C' = [n,k' > k+1, d'], can be converted into a quantum code of parameters [[ n, k+k' - n, min(d, 3d'/2) ]]. This is a generalisation of a previous construction, it enables many new codes of good efficiency to be discovered. Examples based on classical Bose Chaudhuri Hocquenghem (BCH) codes are discussed.
12 pages. Submitted to IEEE Trans. Inf. Theory. Mistake in proof corrected
12 pages. Submitted to IEEE Trans. Inf. Theory. Mistake in proof corrected